Who is using jQuery?
jQuery is implemented as used by some of the biggest companies in the world including Google, Dell, Bank of America, Major League Baseball (MLB), Mozilla, CBS, NBC, Netflix, Wordpress and Drupal to name a few. It's implementation is ever growing, it's lightweight (at only 29k compressed) and is really easy to use and extend, to provide stunning online animations and interactions.
What about cross browser capabilities?
jQuery has been designed to be cross browser compatible. It is compaitble with Internet Explorer (v6.0 +), Mozilla Firefox (v2.0 +), Safari (v3.0 +), Opera (v9.0 +) and Google Chrome. It also has native support for CSS 1-3 selectors. It helps speed up development time, whilst ensuring development is carried out with a standard in place.
Themes and Skinning
jQuery also has a superb rnage of ready use, framework dependent UI components, that can be implemented by a technical development team, but easily skinned by a non-technical team Take a look at the jQuery UI Themeroller tool, to get an idea of the flexibility and capabilities that jQuery can offer your products or projects.